where \(|k \rangle \)  is a feasible state whose objective function value is \(\epsilon _k=\langle k| H_C |k \rangle \) . \(F(\epsilon _k)=\sum _{p<k}|\langle \psi _F(\vec{\gamma },\vec{\beta }) | p \rangle |^2\)  is the cumulative distribution function of \(\epsilon _k\) , where all sum over states are meant in ascending order \(\epsilon _k\) . It could be straightforwardly computed by accessing the wavefunction of the final state, or its sampling statistics.
Metrics that are more focused on the high-quality solutions portion of the probability, such as our (REF ), or the Conditional Value at Risk (CVaR) [1]}, [2]} or Gibbs averages [3]}, are suspected to have some desirable “trainability” properties to guide parameter setting, as opposed to the more traditional \(\langle \psi _F(\vec{\gamma },\vec{\beta }) | H_C | \psi _F(\vec{\gamma },\vec{\beta })\rangle \)  [4]} (which is simply \(\langle \mathrm {BEST}_1\rangle \) ). For illustration, we will work with \(\langle \mathrm {BEST}_5\rangle \) , since \(R=5\)  seems to be a reasonable value to use to reach good approximation ratios for the moderate sizes of problems that we are studying, as we will demonstrate empirically ex-post.
